
DPTCON(l) ) DPTCON(l)
NAME
DPTCON  compute the reciprocal of the condition number (in the 1norm) of a real symmet
ric positive definite tridiagonal matrix using the factorization A = L*D*L**T or A =
U**T*D*U computed by DPTTRF
SYNOPSIS
SUBROUTINE DPTCON( N, D, E, ANORM, RCOND, WORK, INFO )
INTEGER INFO, N
DOUBLE PRECISION ANORM, RCOND
DOUBLE PRECISION D( * ), E( * ), WORK( * )
PURPOSE
DPTCON computes the reciprocal of the condition number (in the 1norm) of a real symmetric
positive definite tridiagonal matrix using the factorization A = L*D*L**T or A = U**T*D*U
computed by DPTTRF. Norm(inv(A)) is computed by a direct method, and the reciprocal of
the condition number is computed as
RCOND = 1 / (ANORM * norm(inv(A))).
ARGUMENTS
N (input) INTEGER
The order of the matrix A. N >= 0.
D (input) DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the diagonal matrix D from the factorization of A, as
computed by DPTTRF.
E (input) DOUBLE PRECISION array, dimension (N1)
The (n1) offdiagonal elements of the unit bidiagonal factor U or L from the fac
torization of A, as computed by DPTTRF.
ANORM (input) DOUBLE PRECISION
The 1norm of the original matrix A.
RCOND (output) DOUBLE PRECISION
The reciprocal of the condition number of the matrix A, computed as RCOND =
1/(ANORM * AINVNM), where AINVNM is the 1norm of inv(A) computed in this routine.
WORK (workspace) DOUBLE PRECISION array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
FURTHER DETAILS
The method used is described in Nicholas J. Higham, "Efficient Algorithms for Computing
the Condition Number of a Tridiagonal Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1,
January 1986.
LAPACK version 3.0 15 June 2000 DPTCON(l) 
